The number of values of x for which sin-1 x2-x4-3-x 6-9- -cos-1 x4-x8-3-x 12-9- - -2- where 0- - x - -3- is

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Trigonometric Equations

The number of...

Question

The number of values of $x$ for which ${sin}^{- 1} (x^{2} - \frac{x^{4}}{3} + \frac{x^{6}}{9} . . .) + {cos}^{- 1} (x^{4} - \frac{x^{8}}{3} + \frac{x^{12}}{9} . . .) = \frac{π}{2}$ , where $0 \leq | x | < \sqrt{3}$ , is

Open in App

Solution

The solutions for the above equations are
$0, 1$ and $(- 1)$
Since $x = - 1$ gives the same result as $x = 1$ due to even powers of x.
Hence 3 real solutions.

Suggest Corrections

Similar questions

Q. Number of value(s) of

x

for which

{sin}^{- 1} (x^{2} - \frac{x^{4}}{3} + \frac{x^{6}}{9} . . .) + {cos}^{- 1} (x^{4} - \frac{x^{8}}{3} + \frac{x^{12}}{9} . . .) = \frac{π}{2}

, where

0 \leq | x | < 3^{1 / 4}

, is

Q. If

sin^{- 1} (x - \frac{x}{2} + \frac{x^{3}}{4} - . . .) + {cos}^{- 1} (x^{2} - \frac{x^{4}}{2} + \frac{x^{6}}{4} - . . .) = \frac{π}{2}

for

0 < | x | < \sqrt{2}

, then

x

equals

Q. If

{sin}^{- 1} (x - \frac{x^{2}}{2} + \frac{x^{3}}{4} - . . . \infty) + {cos}^{- 1} (x^{2} - \frac{x^{4}}{2} + \frac{x^{6}}{4} - . . . \infty) = \frac{π}{2}

for

0 < | x | < \sqrt{2}

,then

x

equal

Q. If

S i n^{- 1} (x - \frac{x^{2}}{2} + \frac{x^{3}}{4} . . . . . \infty) + C o s^{- 1} (x^{2} - \frac{x^{4}}{2} + \frac{x^{6}}{4} . . . . \infty) = \frac{π}{2} f o r 0 < | x | < \sqrt{2}

Then x =___

If $s i n^{- 1} (x - \frac{x^{2}}{2} + \frac{x^{3}}{4} - \dots) + c o s^{- 1} (x^{2} - \frac{x^{4}}{2} + \frac{x^{6}}{4} - \dots) = \frac{π}{2}$ for 0 < 1x < $\sqrt{2}$ , then x equals

Join BYJU'S Learning Program

The number of values of x for which sin−1(x2−x43+x69...)+cos−1(x4−x83+x129...)=π2, where 0≤|x|<√3, is

The solutions for the above equations are0,1 and (−1)Since x=−1 gives the same result as x=1 due to even powers of x.Hence 3 real solutions.

The number of values of $x$ for which ${sin}^{- 1} (x^{2} - \frac{x^{4}}{3} + \frac{x^{6}}{9} . . .) + {cos}^{- 1} (x^{4} - \frac{x^{8}}{3} + \frac{x^{12}}{9} . . .) = \frac{π}{2}$ , where $0 \leq | x | < \sqrt{3}$ , is

The solutions for the above equations are
$0, 1$ and $(- 1)$
Since $x = - 1$ gives the same result as $x = 1$ due to even powers of x.
Hence 3 real solutions.